locus problem

Let the point on the axes be (r,s) and the mid point be (x,y)
we get x=(r+2) /2 y=(s+3) /2

as the segment terminate at coordinate axes,
for point at x-axis, y-coordinate = 0, so s =0
we get the locus is y = 3/2

for point at y-axis, x-coordinate = 0, so r =0
we get the locus is x = 1